Question: Simplify the following expression: $ a = \dfrac{-6n + 4}{-3n + 7} + \dfrac{3}{7} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-6n + 4}{-3n + 7} \times \dfrac{7}{7} = \dfrac{-42n + 28}{-21n + 49} $ Multiply the second expression by $\dfrac{-3n + 7}{-3n + 7}$ $ \dfrac{3}{7} \times \dfrac{-3n + 7}{-3n + 7} = \dfrac{-9n + 21}{-21n + 49} $ Therefore $ a = \dfrac{-42n + 28}{-21n + 49} + \dfrac{-9n + 21}{-21n + 49} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{-42n + 28 - 9n + 21}{-21n + 49} $ $a = \dfrac{-51n + 49}{-21n + 49}$ Simplify the expression by dividing the numerator and denominator by -1: $a = \dfrac{51n - 49}{21n - 49}$